The Eleatic School is an early Pre-Socratic school of philosophy founded by Parmenides in the 5th Century B.C. at Elea, a Greek colony in southern Italy. Other important members of the school include Zeno of Elea, Melissus of Samos (born c. 470 B.C.) and (arguably) the earlier Xenophanes of Colophon (570 – 480 B.C.)
Xenophanes in particular criticized the belief in a pantheon of anthropomorphic gods which was then current, and Parmenides developed his ideas further, concluding that the reality of the world is "One Being", an unchanging, timeless, indestructible whole, in opposition to the theories of the early physicalist philosophers. Later, he became an early exponent of the duality of appearance and reality, and his work was highly influential on later Platonic metaphysics.
Zeno of Elea is best known for his paradoxes (see the Paradoxes section of the page on Logic). But Aristotle has also called him the inventor of the dialectic (the exchange of propositions and counter-propositions to arrive at a conclusion), and Bertrand Russell credited him with having laid the foundations of modern Logic.
The Eleatics rejected the epistemological validity of sense experience, preferring reason and logical standards of clarity and necessity to be the criteria of truth. Parmenides and Melissus generally built their arguments up from indubitably sound premises, while Zeno primarily attempted to destroy the arguments of others by showing their premises led to contradictions ("reductio ad absurdum").
Although the conclusions of the Eleatics were largely rejected by the later Pre-Socratic and Socratic philosophers, their arguments were taken seriously, and they are generally credited with improving the standards of discourse and argument in their time.